SOLUTION: Someone please help me to factor this quadratic expression completely, and find the root of the expression. 49x2 - 14x

SOLUTION: Someone please help me to factor this quadratic expression completely, and find the root of the expression. 49x2 - 14x - 3 Thank you very much.

Question 144571: Someone please help me to factor this quadratic expression completely, and find the root of the expression. 49x2 - 14x - 3 Thank you very much.
Answer by jim_thompson5910(35256) (Show Source): You can put this solution on YOUR website!
First let's factor

Looking at we can see that the first term is and the last term is where the coefficients are 49 and -3 respectively.

Now multiply the first coefficient 49 and the last coefficient -3 to get -147. Now what two numbers multiply to -147 and add to the middle coefficient -14? Let's list all of the factors of -147:

Factors of -147:
1,3,7,21,49,147

-1,-3,-7,-21,-49,-147 ...List the negative factors as well. This will allow us to find all possible combinations

These factors pair up and multiply to -147
(1)*(-147)
(3)*(-49)
(7)*(-21)
(-1)*(147)
(-3)*(49)
(-7)*(21)

note: remember, the product of a negative and a positive number is a negative number

Now which of these pairs add to -14? Lets make a table of all of the pairs of factors we multiplied and see which two numbers add to -14

First Number	Second Number	Sum
1	-147	1+(-147)=-146
3	-49	3+(-49)=-46
7	-21	7+(-21)=-14
-1	147	-1+147=146
-3	49	-3+49=46
-7	21	-7+21=14

From this list we can see that 7 and -21 add up to -14 and multiply to -147

Now looking at the expression , replace with (notice adds up to . So it is equivalent to )

Now let's factor by grouping:

Group like terms

Factor out the GCF of out of the first group. Factor out the GCF of out of the second group

Since we have a common term of , we can combine like terms

So factors to

Set the factored expression equal to zero

Now set each factor equal to zero:

or

or Now solve for x in each case

So our answers are

or

RELATED QUESTIONS
I could really use some help. Factor the quadratic expression completely, and find the... (answered by checkley71)

factor completely and find the root of the expression 49x^2 -14x -3 Can you please... (answered by Alan3354,htmentor)

factor the quadratic expression completely, and find the roots of the expression.... (answered by vidhyak)

Hello everyone, I need help please? Completely factor the following expression: 49x2... (answered by Gogonati)

How would you factor this quadratic expression completely, so you can find the roots of... (answered by vleith)

I really could use some help on this one. Please! Please factor the quadratic... (answered by checkley71)

48x^2y+72xy^2+27y^3 Completely factor the expression Please someone walk me through... (answered by Edwin McCravy)

I'm really lost on this one when it comes to finding the roots, hopefully I'm on the... (answered by venugopalramana)

This problem I must factor the quadratic expression completely, and find the roots of the (answered by philline_palana)